Question 64
Can we find ten sets $A_1, A_2, \dots, A_{10}$ such that
(i) Each set is in the form of $\{a, b, c\}$, where $a \in \{1, 2, 3\}$, $b \in \{4, 5, 6\}$, $c \in \{7, 8, 9\}$.
(ii) Each set is different to any other.
(iii) If we place the sets into a circle ($A_1, A_2, \dots, A_{10}$), then any pair of neighbouring sets has no common element, but any pair of non-neighbouring sets does? (Remark. $A_{10}$ is a neighbour of $A_1$.)
(i) Each set is in the form of $\{a, b, c\}$, where $a \in \{1, 2, 3\}$, $b \in \{4, 5, 6\}$, $c \in \{7, 8, 9\}$.
(ii) Each set is different to any other.
(iii) If we place the sets into a circle ($A_1, A_2, \dots, A_{10}$), then any pair of neighbouring sets has no common element, but any pair of non-neighbouring sets does? (Remark. $A_{10}$ is a neighbour of $A_1$.)